Developing Literal Expressions

This page focuses on developing literal expressions, which is the inverse process of factorization.

Simple Development

Definition: Developing a literal expression means transforming a product into a sum or difference.

The general forms for simple development are:

K(a + b) = K × a + K × b = Ka + Kb K(a - b) = K × a - K × b = Ka - Kb

Where K, a, and b are numbers.

Example: 3(x + 2) = 3 × x + 3 × 2 = 3x + 6

Several examples are provided to illustrate this concept:

1. 5(5 - x) = 5 × 5 - 5 × x = 25 - 5x
2. x(x + 4) = x × x + x × 4 = x² + 4x
3. 3x(4 - 2) = 3x × 4 - 3x × 2 = 12x - 6x

Double Development

The page also introduces the concept of double development, which involves multiplying two binomials.

Highlight: The general form for double development is: (a + b)(c + d) = a × c + a × d + b × c + b × d = ac + ad + bc + bd

Where a, b, c, and d are numbers.

This formula is crucial for développer et réduire exercices corrigés and is often featured in calcul littéral 3ème exercices corrigés.

Vocabulary: Binomial - An algebraic expression consisting of two terms.

Understanding these concepts of developing literal expressions is essential for mastering calcul littéral 3ème and preparing for more advanced algebraic manipulations in higher grades.